Let t, s, h, r, and c be the following propositions: t: I will play tennis. s: It is sunny. h: I stay home. r: I read a book. c: I will bike in a park.

1. Express the following propositions as English sentences: a) h r b) s t c) Assume s c, write the Contrapositive (c s) d) Assume s c, write the Converse (c s) e) Assume s c, write the Inverse (s c) 2. Express each of these statements using quantifiers and . Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. a) There is a cat that can add. b) Every koala can climb. c) No monkey can speak French. d) Every rational number can be written as a ratio of some two integers. 3. Using the truth table Determine whether: a) (p q ) (p q) is equivalent to p p b) p (p q) is equivalent to p q 4. Show the following statement is contraction, a tautology, or neither. (p(qr)) (p q r)

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